It's probably a bit boring to say so, but I do think that even for an old computer, it's best to stay within the ecosystem of the Ubuntu LTS official flavours. Of those, Lubuntu is probably the most lightweight.

ive never distro hopped to that one but is it really lighter than peppermint 9, as a for instance, ...the reason i ask this is because on my 11 year old asus eee pc with just 1 gig of ram and an atom 1.66 ghz processor, (i purposely have not increased the ram on this so i can really stress it out), (i use this for testing only) i can comfortably run peppermint 9 and even stream videos without glitching as long as im not doing anything else at the same time...just wondering is all and if you have tried this distro as well...DAMIEN

I use Lubuntu 18.04 on a similarly spec'ed netbook as your eeePc, and whilst not very fast, it is very usable.
On cold boot it uses about 150 - 170MB ram; I have no idea how lean Peppermint is so will have to leave you to deal with that comparison.

Generally the problem with low spec machines is the applications you use, not necessarily the OS/DE itself, so, for example, LibreOffice would be an unwise office-suite on that machine, and firefox or chromium may also be too heavy, though I'm not sure what other real choice you have, or what to use as a light web-browser.

Peppermint is based on Ubuntu but has elements from Mint, such as Mint's update manager. I've run both Lubuntu and Peppermint and much prefer the latter, as it has many more features and is nearly as lightweight. Peppermint combines elements of both LXDE and Xfce, but they are gradually shifting away from LXDE.

“Three o'clock is always too late or too early for anything you want to do.”
― Jean-Paul Sartre

I have tested the following distros (in order of lightness) looking for the lightest 32-bit distro for my very old, single-core laptop:

- Puppy Xenial (stripped off of features to the point it's so inconvenient for use)
- Bodhi (could not make it to work on the actual machine it was intended for)
- antiX (I ended up using this one)
- LXLE
- Lubuntu
- Linux Mint Xfce 18.3
- MX
- Linux Lite

If you're looking for a greener Linux pasture, you won't find any that is greener than Linux Mint. ;)

It's probably a bit boring to say so, but I do think that even for an old computer, it's best to stay within the ecosystem of the Ubuntu LTS official flavours. Of those, Lubuntu is probably the most lightweight.

Nothing beats the advantages of the Ubuntu LTS codebase.

It's not boring; after taking a look at some of the distros mentioned I think your point is valid.